Which graph represents the following piecewise defined function?
2 answers:
The correct answer is shown in attached figure
To find the correct graph, we should study the continuity of the function
Check the continuity at x = -2
from the left ⇒⇒ f(-2) = 1/2 * -2 + 3 = 2
from the right ⇒⇒ f(-2) = 2
∴ The function is continuous at x = -2
Check the continuity at x = 3
from the left ⇒⇒ f(3) = 2
from the right ⇒⇒ f(3) = 2*3 - 3 = 3
∴ The function is jump discontinuous at x = 3
From the previous results the correct graph is the last as shown in attached graph.
To find the correct graph, we should study the continuity of the function
Check the continuity at x = -2
from the left ⇒⇒ f(-2) = 1/2 * -2 + 3 = 2
from the right ⇒⇒ f(-2) = 2
∴ The function is continuous at x = -2
Check the continuity at x = 3
from the left ⇒⇒ f(3) = 2
from the right ⇒⇒ f(3) = 2*3 - 3 = 3
∴ The function is jump discontinuous at x = 3
From the previous results the correct graph is the last as shown in attached graph.
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So firstly, you want to multiply both sides by (x-2)(x+2) since it is the LCM, or lowest common multiplier. Your equation will look like this:
Next, you can cancel out the denominators on 3/x+2 and 4/x-2 on the left side:
Next, foil:
Next, combine like terms:
Next, add x + 14 on both sides:
Next, replace x with -5x + 6x:
Next, factor 5x^2-5x and 6x-6 separately. Make sure that both factors have the same quantity within the parentheses:
With this, we can rewrite it as From here, we solve for x in (5x+6) and (x-1) separately and setting them to zero.
In short, x = -1.2, 1.